Improved Approximation Algorithms for Box Contact Representations

We study the following geometric representation problem: Given a graph whose vertices correspond to axis-aligned rectangles with fixed dimensions, arrange the rectangles without overlaps in the plane such that two rectangles touch if the graph contains an edge between them. This problem is called Contact Representation of Word Networks (Crown) since it formalizes the geometric problem behind drawing word clouds in which semantically related words are close to each other. Crown is known to be NP-hard, and there are approximation algorithms for certain graph classes for the optimization version, Max-Crown, in which realizing each desired adjacency yields a certain profit. We present the first O(1)-approximation algorithm for the general case, when the input is a complete weighted graph, and for the bipartite case. Since the subgraph of realized adjacencies is necessarily planar, we also consider several planar graph classes (namely stars, trees, outerplanar, and planar graphs), improving upon the known results. For some graph classes, we also describe improvements in the unweighted case, where each adjacency yields the same profit. Finally, we show that the problem is APX-complete on bipartite graphs of bounded maximum degree. © 2016, Springer Science+Business Media New York

To what degree have the non-police public services adopted the National Intelligence Model? : what benefits could the National Intelligence Model deliver?

It is claimed that the National Intelligence Model (NIM) consolidated intelligence-led policing principles in investigative practice and decision making in British policing. Subsequently, encouraged by the Home Office, the NIM was adopted by a number of other public services with an investigative capability. However, that transfer took place without a sufficiently rigorous evaluation of the model’s value to the police service and without any meaningful analysis of its relevance to the investigative functions of other public sector agencies. This research examined the adoption of the NIM by three public sector bodies: The Department for Work and Pensions (DWP), The Identity and Passport Service (IPS) and the Driving Standards Agency (DSA). It drew on archival materials, associated literature and the analysis of semi-structured interviews with the personnel of these and associated agencies. Research respondents also assessed a simplified version of the NIM that was designed to remove many of the original model’s inconsistencies and ambiguities. The research identified that the reviewed public services are not compliant with the NIM minimum standards and that the model has not delivered any meaningful improvement in the consistency of process, investigative efficiency, improved partnership working, or in fraud reduction in those agencies. The NIM failed because of perceived complexity, the language of the model and supplementary guidance; its exclusive ‘fit’ with the police; and a suspicion by the agencies’ personnel that its adoption was intended as a performance management and governance tool. Moreover, the revised version of the NIM’s minimum standards did not improve comprehension or conformity, or resolve the model’s perceived police bias. It was concluded that the model is not fit for purpose for the agencies studied and that an alternative model that is more finely tuned to the needs of those agencies is required.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

(r,p)-centroid problems on paths and trees

AbstractAn instance of the (r,p)-centroid problem is given by an edge and node weighted graph. Two competitors, the leader and the follower, are allowed to place p and r facilities, respectively, into the graph. Users at the nodes connect to the closest facility. A solution of the (r,p)-centroid problem is a leader placement such that the maximum total weight of the users connecting to any follower placement is as small as possible.We show that the absolute (r,p)-centroid problem is NP-hard even on a path which answers a long-standing open question of the complexity of the problem on trees (Hakimi, 1990 [10]). Moreover, we provide polynomial time algorithms for the discrete (r,p)-centroid on paths and the (1,p)-centroid on trees, and complementary hardness results for more complex graph classes

Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity

| openaire: EC/H2020/759557/EU//ALGOComWe initiate the study of the following natural geometric optimization problem. The input is a set of axis-aligned rectangles in the plane. The objective is to find a set of horizontal line segments of minimum total length so that every rectangle is stabbed by some line segment. A line segment stabs a rectangle if it intersects its left and its right boundary. The problem, which we call Stabbing, can be motivated by a resource allocation problem and has applications in geometric network design. To the best of our knowledge, only special cases of this problem have been considered so far. Stabbing is a weighted geometric set cover problem, which we show to be NP-hard. While for general set cover the best possible approximation ratio is (log n), it is an important field in geometric approximation algorithms to obtain better ratios for geometric set cover problems. Chan et al. [SODA’12] generalize earlier results by Varadarajan [STOC’10] to obtain sub-logarithmic performances for a broad class of weighted geometric set cover instances that are characterized by having low shallow-cell complexity. The shallow-cell complexity of Stabbing instances, however, can be high so that a direct application of the framework of Chan et al. gives only logarithmic bounds. We still achieve a constant-factor approximation by decomposing general instances into what we call laminar instances that have low enough complexity. Our decomposition technique yields constant-factor approximations also for the variant where rectangles can be stabbed by horizontal and vertical segments and for two further geometric set cover problems.Peer reviewe

Improved Approximation Algorithms for Box Contact Representations

We study the following geometric representation problem: Given a graph whose vertices correspond to axis-aligned rectangles with fixed dimensions, arrange the rectangles without overlaps in the plane such that two rectangles touch if the graph contains an edge between them. This problem is called Contact Representation of Word Networks (Crown) since it formalizes the geometric problem behind drawing word clouds in which semantically related words are close to each other. Crown is known to be NP-hard, and there are approximation algorithms for certain graph classes for the optimization version, Max-Crown, in which realizing each desired adjacency yields a certain profit. We present the first O(1)-approximation algorithm for the general case, when the input is a complete weighted graph, and for the bipartite case. Since the subgraph of realized adjacencies is necessarily planar, we also consider several planar graph classes (namely stars, trees, outerplanar, and planar graphs), improving upon the known results. For some graph classes, we also describe improvements in the unweighted case, where each adjacency yields the same profit. Finally, we show that the problem is APX-complete on bipartite graphs of bounded maximum degree.ESF EuroGIGA project GraDR; NSF [CCF-1115971, DEB 1053573]12 month embargo; First Online: 27 January 2016This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]